A numerical model has been developed for non-equilibrium solidification in welds that considers momentum, heat and solute transport. The model uses an effective partition coefficient, which considers both the local interface velocity and the undercooling for accurate prediction of solute concentration in the mushy zone. The calculations show that convection plays a dominant role in the solute transport inside the weld pool. The predicted weld metal solute content agreed well with the independent experimental observations. The liquation cracking susceptibility in Al-Cu alloy weldments could be reliably predicted by the model, based on the computed solidifying weld metal composition and the resulting solid fraction considering non-equilibrium solidification.